# There were 100 more balcony tickets then main-floor tickets sold for a concert. The balcony tickets sold for $4 and the main-floor tickets sold for $12. The total amount of sales for both types of tickets was $3,056.

a. write an equations or a system of equations that describes the given situation. define the variables.

b.Find the number of balcony tickets that were sold.

Although I will not solve the problem completely for you, I will tell you the process for reaching the solution. This will mean that you will have to exert a little more effort, time and thinking, but I hope it will help you to learn more.

Let M stand for the number of main-floor tickets sold. Then the number of balcony tickets would be (M + 100). (You could also let B equal the number of balcony tickets and B - 100 for the number of main-floor tickets.)

Thus the money for the balcony tickets with the first version above was $4 (M + 100) and the money for the main-floor tickets was $12 M.

You should be able continue from here.

I hope this helps. Thanks for asking.

## a. The equations or system of equations that describes the given situation is 4(M + 100) + 12M = 3056. The variables are M (the number of main-floor tickets sold) and B (the number of balcony tickets sold).

b. To find the number of balcony tickets that were sold, we can solve the equation 4(M + 100) + 12M = 3056. Solving this equation yields M = 200, so the number of balcony tickets sold is 200 + 100 = 300.

## a. Let M be the number of main-floor tickets sold and let B be the number of balcony tickets sold.

Since there were 100 more balcony tickets sold than main-floor tickets, we can write the equation: B = M + 100.

The balcony tickets sold for $4, so the revenue from balcony ticket sales is given by: Revenue from balcony tickets = $4 * B = $4 * (M + 100) = $4M + 400.

The main-floor tickets sold for $12, so the revenue from main-floor ticket sales is given by: Revenue from main-floor tickets = $12 * M = $12M.

The total amount of sales for both types of tickets is $3056, so we can write the equation: Revenue from main-floor tickets + Revenue from balcony tickets = $3056. This equation can be represented as:

$12M + $4M + $400 = $3056.

b. To find the number of balcony tickets sold (B), we substitute B = M + 100 into the equation $4M + $400 = $3056:

$4M + $400 = $3056.

Solving this equation will give the value of M, which represents the number of main-floor tickets sold. From there, we can find the number of balcony tickets sold (B) by using the equation B = M + 100.

## To solve this problem, we can start by writing an equation or a system of equations that represents the given situation.

Let's define the variables:

M = number of main-floor tickets sold

B = number of balcony tickets sold

According to the problem, there were 100 more balcony tickets sold than main-floor tickets. Therefore, we can write the equation:

B = M + 100 ---(equation 1)

We also know that balcony tickets were sold for $4 each and main-floor tickets were sold for $12 each. The total amount of sales for both types of tickets was $3,056. So, the equation for the total sales can be written as:

4B + 12M = 3056 ---(equation 2)

Now, we have a system of equations consisting of equation 1 and equation 2.

To find the number of balcony tickets sold (B), we can substitute equation 1 into equation 2:

4(M + 100) + 12M = 3056

Now we can solve this equation to find the value of M. Once we have the value of M, we can substitute it back into equation 1 to find the value of B.